What does Luke 8:19 mean?

Matthew places this earlier, but on the same day, as the parable of the sower (Matthew 12:46—13:9). Mark seems to say Jesus is at home (Mark 3:20), which probably means Peter and Andrew's house in Capernaum. Whichever home Jesus is in, it's filled with people to the point that no one else can get in.

In fact, so many people have been trying to get to Jesus that He doesn't even have time to eat (Mark 3:20). Jesus' family is less concerned about His schedule and more about His mental state: "And when his family heard it, they went out to seize him, for they were saying, 'He is out of his mind'" (Mark 3:21). It's unclear who thinks Jesus is out of His mind, but Mary and Jesus' brothers are concerned. Unwilling to pull the roof apart (Mark 2:1–12), they send a message.

Why are they concerned? The passage doesn't say. As the firstborn male of the family, and Joseph presumably dead, Jesus was responsible for Mary's care and the wellbeing of the family. It might be that the Nazarenes are holding Jesus' family accountable for His behavior, perhaps even threatening them financially (Luke 4:16–30). Or, possibly, the religious leaders who have had unfavorable interactions with Jesus are telling His brothers to pull Him into line.

For Luke, however, the stress is not on the rejection of Jesus by His mother and brothers. He only mentions that the family came and could not get to Jesus, not that they were concerned. Luke is still talking about how important it is to listen to God's Word, a message begun in the parable of the sower (Luke 8:4–8).